Whispering gallery mode (“WGM”) resonators have an extremely high quality factor (“Q”), and therefore a narrow pass band, when used as a filter in telecommunication applications. For example, optical filter 110 of FIG. 1 filters out light at wavelengths at λ1 and λ3, while allowing light at λ2 to pass. Wavelength division multiplexing (“WDM”) has been used to carry multiple signals over one strand of optical fiber by superimposing light waves of different wavelengths. For example, FIG. 2 shows an optical coupler 210 receiving multiple input signals 205 (e.g., in the 1500 nm range) and outputting a multiplexed signal 215. A high density version of WDM, called dense WDM (“DWDM”), has also been implemented to carry more signals (e.g., 40 channels at 100 GHz (˜0.8 nm spacing)) than does the conventional or coarse WDM (“CWDM”) (e.g., 8 channels at 20 nm spacing). The decomposition of signals into individual components at the receiving end relies on filters. For example, referring back to FIG. 2, an optical splitter/filter 220 may be used to separate the superimposed waves to provide multiple output signals 225 corresponding to the multiple input signals 205.
Currently, fiber Bragg gratings (“FBGs”) are widely used as optical filters. FBGs having 0.5 to 1 nanometer (nm) wide wavelength pass bands are known. Unfortunately, however, to decrease the width of the pass band, the physical size of an FBG must be increased. This increased sized makes FBGs impractical for some applications. Further, as the size of an FBG increases, its susceptibility to environmental factors such as changes in ambient temperature increases. Therefore, FBGs become less practical as the packing density of DWDM increases.
The spacing between adjacent channels can be decreased if the width of each of the filters' respective pass band is decreased, for example, by employing high-Q filters. For example, FIG. 3 depicts the narrow pass band λr (e.g., with a width of 0.1 to 0.01 pm and a Q of 107 to 108) of a WGM resonator 310. Unfortunately, however, the precision of the pass band wavelength and its vulnerability to environmental changes becomes a problem as more wavelength components are packed into a given range of wavelength. That is, the pass band wavelength of a WGM resonator may shift, for example due to environmental factors, such as changes in ambient temperature for example. For applications in which many close wavelengths are multiplexed within a narrow range, such a shift in the pass band wavelength becomes unacceptable.
Past studies on tuning the wavelength of a WGM resonator involve the use of piezoelectricity. Such studies include the following references:    1. M. Eichenfield, C. P. Michael, R. Perahia, and O. Painter, Nature Photon. 1, 416 (2007);    2. W. von Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, New J. Phys. 3, 14.1 (2001);    3. G. Farca, S. I. Shopova, and A. T. Rosenberger, Opt. Exp. 15, 17443 (2007);    4. Q. Lin, T. J. Johnson, C. P. Michael, and O. Painter, Opt. Exp. 16, 14801 (2008).    5. J. Rosenberg, Q. Lin, and O. Painter, Nature Photon. 3, 478 (2009);    6. M. Pöllinger, D. O'Shea, F. Warken, and A. Rauschenbeutel, Phys. Rev. Lett. 103, 053901 (2009);    7. D. O'Shea, A. Rettenmaier and A. Rauschenbeutel, Appl. Phys. B 99, 623 (2010); and    8. P. T. Rakich, M. A. Popović, M. Solja{hacek over (c)}ić, E. P. Ippen, Nature Photon. 1, 658 (2007).(Each of the foregoing eight references is incorporated herein by reference.)
Typically, mechanical strain is used to physically deform the WGM resonator, thereby changing the resonance wavelength (by changing the resonator's effective optical path length). As is understood by those having ordinary skill in the art, “optical path length” is defined as a physical length of an optical path * the refractive index of the resonator, and an “effective optical path length” is defined as a physical length of an optical path * the effective refractive index. Unfortunately, systems using mechanical strain to physically deform the WGM resonator use a complicated feedback mechanism to construct a tunable filter or to stabilize the pass band wavelength. It would be useful to avoid such complicated feedback mechanisms. Example embodiments consistent with the present invention avoid such complicated feedback mechanisms.